Using Pasmo or Suica paas

Can I use Pasmo or Suica paas for both Tokyo Metro and Tokyo subway lines ? I want to travel by subway from Kuramae to Nihonbashi . Which pass should I buy ? Pasmo or Suica ?

Either will do, they are essentially interchangeable. Just purchase whichever happens to be on sale at the first station (which will depend on whether it's a JR or a subway station).

More info here:

http://www.japan-guide.com/e/e2359_003.html

Both card works for both area no problem.

But PASMO/Suica and more train IC card(of other area) are NOT "unlimited/discount PASS"
just one of "prepaid" sysytem for train,bus and shopping(as e-money) by charge(SF:stored fare/balance)
very convenient every purchasing at ticket vending machine process skip and not be flood by coins.

PASMO sales/refunds by non JR group (railway and bus companies)
Suica sales/refunds by JR-East (railway only, no bus company)

Read both official web and guides[PDF]
http://www.pasmo.co.jp/en/
http://www.jreast.co.jp/e/pass/suica.html
and search regular train/subway fare/transfer.
http://www.hyperdia.com/en/

(note)
No "Tokyo subway" subway lines goup in Tokyo "Tokyo Metro" and "Toei".
http://www.tokyometro.jp/en/index.html
http://www.kotsu.metro.tokyo.jp/eng/
Metro and Toei are not same railway company.